--- a/progs/re4.scala	Wed Oct 02 00:10:52 2013 +0100
+++ b/progs/re4.scala	Wed Oct 02 01:02:50 2013 +0100
@@ -1,4 +1,5 @@
 import scala.annotation.tailrec    
+    
 abstract class Rexp {
   def simp : Rexp = this
 }
@@ -12,7 +13,7 @@
     case (r, NULL) => r
     case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
     case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
-    case (r1, r2) => ALT(r1, r2)
+    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
   }
 }
 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
@@ -24,8 +25,21 @@
     case (r1, r2) => SEQ(r1, r2)
   }
 }
-case class STAR(r: Rexp) extends Rexp 
-case class NTIMES(r: Rexp, n: Int) extends Rexp 
+case class STAR(r: Rexp) extends Rexp {
+  override def simp = r.simp match {
+    case NULL => EMPTY
+    case EMPTY => EMPTY
+    case r => STAR(r)
+  }
+}
+case class NTIMES(r: Rexp, n: Int) extends Rexp {
+  override def simp = if (n == 0) EMPTY else 
+    r.simp match {
+      case NULL => NULL
+      case EMPTY => EMPTY
+      case r => NTIMES(r, n)
+    }
+}
 
 // some convenience for typing in regular expressions
 def charlist2rexp(s : List[Char]) : Rexp = s match {
@@ -45,7 +59,7 @@
   case ALT(r1, r2) => nullable(r1) || nullable(r2)
   case SEQ(r1, r2) => nullable(r1) && nullable(r2)
   case STAR(_) => true
-  case NTIMES(r, i) => if (i == 0) false else nullable(r)
+  case NTIMES(r, i) => if (i == 0) true else nullable(r)
 }
 
 // derivative of a regular expression w.r.t. a character
@@ -73,18 +87,10 @@
 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
 
-
 //one or zero
 def OPT(r: Rexp) = ALT(r, EMPTY)
 
-//n-times
-/*def NTIMES(r: Rexp, n: Int) : Rexp = n match {
-  case 0 => NULL
-  case 1 => r
-  case n => SEQ(r, NTIMES(r, n - 1))
-}*/
-
-def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
+def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -94,8 +100,8 @@
 }
 
 
-for (i <- 1 to 13001 by 500) {
-  println(i + " " + time_needed(1, matcher(RTEST(i), "a" * i)))
+for (i <- 1 to 12001 by 500) {
+  println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i))))
 }